Spread field imaging collimators for radiation-based imaging and methods of using the same

ABSTRACT

A radiation-based imaging system includes a collimator configured to filter radiation emitted from a target object, the collimator including a plurality of apertures non-uniformly distributed on the collimator. A largest acceptance angle of the plurality of apertures is not larger than 15°. The radiation-based imaging system further includes a detector for detecting the radiation that has passed through the collimator. The collimator is spaced from the detector such that a point on a top surface of the detector that faces the collimator is simultaneously illuminated by two or more of the plurality of apertures.

PRIORITY

This claims the benefits of and priority to U.S. Provisional ApplicationSer. No. 63/168,778 filed Mar. 31, 2021 and U.S. Provisional ApplicationSer. No. 63/071,540 filed Aug. 28, 2020, the entire disclosure of whichis herein incorporated by reference.

BACKGROUND

In radiation-based imaging, such as molecular medical imaging (sometimesknown as nuclear medicine imaging), images representingradiopharmaceutical distributions may be generated for medicaldiagnosis. Prior to imaging, radiopharmaceuticals are injected into atarget object such as a patient. The radiopharmaceuticals emitradioactive photons, which can penetrate through the body to be detectedby a photon detector. Based on information from the received photons,the photon detector may then determine the distribution of theradiopharmaceuticals inside the patient. The distribution represents thephysiological function of the patient, and therefore images of thedistribution provide valuable clinical information for diagnosis of avariety of diseases and conditions such as those in cardiology,oncology, neurology, etc.

To generate images, collimator and photon detector work in tandem. Acollimator is a device that guides photon path (i.e., guides photon totake certain path). In radiation-based imaging, photons may originatefrom unknown locations inside a subject, unlike in X-ray or CT wherephotons are emitted from a known source (or sources) position. Withoutcollimators, photons from all directions may be recorded by a photondetector, and image reconstruction may become difficult. Therefore,collimators are employed to guide possible photon paths so that imagescan be reconstructed, similar to the role of lens in a photographycamera. Although existing radiation-based imaging systems have beengenerally adequate for their intended purposes, they have not beenentirely satisfactory in all respects. For example, existing collimatorsand detectors often have to be deployed with a tradeoff between imagingresolution and signal sensitivity, but not excel in both. Therefore,improvements on radiation-based imaging systems are desired.

SUMMARY

According to various embodiments, the present disclosure provides aradiation-based imaging system. The radiation-based imaging systemincludes a collimator configured to filter radiation emitted from atarget object, the collimator including a plurality of aperturesnon-uniformly distributed on the collimator, wherein a largestacceptance angle of the plurality of apertures is not larger than 15°;and a detector for detecting the radiation that has passed through thecollimator, wherein the collimator is spaced from the detector, suchthat a point on a top surface of the detector that faces the collimatoris simultaneously illuminated by two or more of the plurality ofapertures. In some embodiments, a point on the top surface of thedetector is simultaneously illuminated by a percentage of the pluralityof apertures, wherein the percentage is less than about 25%. In someembodiments, an amount of the plurality of apertures exceeds onethousand. In some embodiments, the plurality of apertures varies atleast in one of aperture size, aperture shape, acceptance angle, length,and aperture pitch. In some embodiments, a distance between thecollimator and the detector is from about 0.5 to about 10 times (such asfrom 1.5 to 10 times) of a thickness of the collimator. In someembodiments, the plurality of apertures forms a pattern that includes arepetitive basic pattern. In some embodiments, the repetitive basicpattern is a coded aperture pattern. In some embodiments, anilluminating area of one of the apertures substantially equals to anarea of the repetitive basic pattern. In some embodiments, thecollimator includes a first portion and a second portion, wherein thefirst portion includes through-holes uniformly distributed on the firstportion and the second portion includes through-holes non-uniformlydistributed on the second portion and corresponding to the plurality ofapertures, such that a portion of the through-holes of the first portionis blocked by the second portion. In some embodiments, a thickness ofthe first portion is from about 2 to about 10 times of a thickness ofthe second portion. In some embodiments, the collimator is a firstcollimator and the detector is a first detector, the system furtherincludes a second collimator and a second detector coupled to the secondcollimator, wherein the second collimator is attached to the seconddetector.

According to various embodiments, the present disclosure provides aradiation-based imaging system. The radiation-based imaging systemincludes a first collimator configured to filter radiation emitted froma target object, the first collimator including a first plurality ofapertures that forms a first aperture pattern; a first detectorassociated with the first collimator for detecting the radiation thathas passed through the first collimator; a second collimator configuredto filter the radiation emitted from the target object, the secondcollimator including a second plurality of apertures that forms a secondaperture pattern; and a second detector associated with the secondcollimator for detecting the radiation that has passed through thesecond collimator, wherein the target object is positioned between thefirst collimator and the second collimator, and wherein the firstaperture pattern is different from the second aperture pattern. In someembodiments, the first collimator is in contact with the first detector,and wherein the second collimator is spaced from the second detector. Insome embodiments, a distance between the second collimator and thesecond detector is from about 0.5 to about 7 times (such as from 1.5 to7 times) of a thickness of the second collimator. In some embodiments,the first plurality of apertures is uniformly distributed on the firstcollimator, and wherein the second plurality of apertures isnon-uniformly distributed on the second collimator. In some embodiments,the second aperture pattern includes a repetitive coded pattern. In someembodiments, the repetitive coded pattern is one of a uniformlyredundant array (URA) pattern, a modified uniformly redundant array(MURA) pattern, and a perfect binary array (PBA) pattern. In someembodiments, directions the first and second detectors pointing towardhave an offset angle.

According to various embodiments, the present disclosure provides acollimator for filtering radiation emitted by an object. The collimatorincludes a first portion including a first plurality of through-holesthat are uniformly distributed; and a second portion including a secondplurality of through-holes that are non-uniformly distributed, whereinthe first and second portions are spaced apart and aligned in a way thatphotons emitted by the object traveling through some of the firstplurality of through holes are blocked by the second portion. In someembodiments, the second plurality of through-holes forms a codedpattern. In some embodiments, the second portion is operable to slidewith respect to a surface of the first portion facing the secondportion, such that the aligned through-holes of the first and secondpluralities of through-holes can be changed.

According to various embodiments, the present disclosure provides amethod of misalignment correction in an imaging system. The methodincludes providing a collimator and a detector, the detector having adigitized pixel grid; illuminating the collimator with a flood lightsource; recording signal intensities in each pixel of the digitizedpixel grid, wherein the signal intensities are caused by theilluminating of the collimator; deriving a descriptor from the recordedsignal intensities; generating a series of offsets introduced to thedigitized pixel grid; finding a selected offset from the series ofoffsets that optimizes the descriptor; and regenerating the digitizedpixel grid based on an actual optimum offset derived from the selectedoffset. In some embodiments, the selected offset includes a pair ofoffset values in two orthogonal directions, respectively. In someembodiments, the descriptor is one of a contrast value, a peak value,and a valley value of the recorded signal intensities. In someembodiments, the contrast value is determined by a ratio of values atpeaks and valleys of a signal intensity line corresponding to the signalintensities recorded at the digitized pixel grid. In some embodiments,the finding of the selected offset includes sweeping the series ofoffsets and picking the selected offset that maximizes or minimizes thedescriptor. In some embodiments, the regenerating the digitized pixelgrid includes adjusting the selected offset by a fixed offset togenerate the actual optimum offset and regenerating the digitized pixelgrid with the actual optimum offset.

BRIEF DESCRIPTION OF THE DRAWINGS

The present disclosure is best understood from the following detaileddescription when read with the accompanying figures. It is emphasizedthat, in accordance with the standard practice in the industry, variousfeatures are not drawn to scale and are used for illustration purposesonly. In fact, the dimensions of the various features may be arbitrarilyincreased or reduced for clarity of discussion.

FIGS. 1A, 1B, and 1C are schematic diagrams of an exemplaryradiation-based imaging system according to various aspects of thepresent disclosure.

FIGS. 2A, 2B, 2C, 2D, 2E, and 2F provide perspective, cross-sectional,and top views of part of a collimator according to some embodiments ofthe present disclosure.

FIG. 3 is a cross-sectional view of part of a radiation-based imagingsystem according to some embodiments of the present disclosure.

FIG. 4 is a cross-sectional view of part of a radiation-based imagingsystem according to some other embodiments of the present disclosure.

FIGS. 5A and 5B illustrate top views of part of a collimator withnon-uniformly distributed apertures according to various aspects of thepresent disclosure.

FIGS. 6A, 6B, and 6C illustrate top views of a collimator with arepetitive basic pattern according to some embodiments of the presentdisclosure.

FIG. 7 illustrates a step of decomposing an original image into a seriesof sub-images in a fast image reconstruction algorithm according tovarious aspects of the present disclosure.

FIGS. 8A, 8B, 8C, 9A, 9B, 9C, 10A, and 10B illustrate cross-sectionalviews of some embodiments of light-weight collimators according to someembodiments of the present disclosure.

FIGS. 11A, 11B, 12A, 12B, and 13 illustrate top views andcross-sectional views of some embodiments of radiation-based imagingsystems with alignment adjustment.

DETAILED DESCRIPTION

The following disclosure provides many different embodiments, orexamples, for implementing different features of the disclosure.Specific examples of components and arrangements are described below tosimplify the present disclosure. These are, of course, merely examplesand are not intended to be limiting. Any alterations and furthermodifications to the described devices, systems, methods, and anyfurther application of the principles of the present disclosure arefully contemplated as would normally occur to one having ordinary skillin the art to which the disclosure relates. For example, the features,components, and/or steps described with respect to one embodiment may becombined with the features, components, and/or steps described withrespect to other embodiments of the present disclosure to form yetanother embodiment of a device, system, or method according to thepresent disclosure even though such a combination is not explicitlyshown. In addition, the present disclosure may repeat reference numeralsand/or letters in the various examples. This repetition is forsimplicity and clarity and does not in itself dictate a relationshipbetween the various embodiments and/or configurations discussed.

Moreover, a feature on, connected to, and/or coupled to another featurein the present disclosure that follows may include embodiments in whichthe features are in direct contact, and may also include embodiments inwhich additional features may interpose the features, such that thefeatures may not be in direct contact. In addition, spatially relativeterms, for example, “lower,” “upper,” “horizontal,” “vertical,” “above,”“over,” “below,” “beneath,” “up,” “down,” “top,” “bottom,” etc., as wellas derivatives thereof (e.g., “horizontally,” “downwardly,” “upwardly,”etc.) are used for ease of the present disclosure of one featuresrelationship to another feature. The spatially relative terms areintended to cover different orientations of the device including thefeatures. Still further, when a number or a range of numbers isdescribed with “about,” “approximate,” and the like, the term isintended to encompass numbers that are within a reasonable rangeincluding the number described, such as within +/−10% of the numberdescribed or other values as understood by person skilled in the art.For example, the term “about 5 cm” encompasses the dimension range from4.5 cm to 5.5 cm.

The present disclosure is generally related to collimators for use inradiation-based imaging, and more particularly to collimators withnon-uniformly distributed apertures for use in nuclear medicine(molecular) imaging systems. The term “non-uniformly distributedapertures” refers to apertures (through-holes) of a collimator that varyin at least one of aperture profiles including but not limited toaperture size, aperture shape (including cross-sectional andlongitudinal shape), aperture length, aperture pitch, and apertureorientation.

In radiation-based imaging, such as nuclear medicine (molecular) imagingsystems, collimator and detector work in tandem to generate images thatrepresent radiopharmaceutical distributions within a subject. Manynuclear medicine imaging systems, for example, single photon emissioncomputed tomography (SPECT), and positron emission tomography (PET)imagining systems, use one or more detectors, to acquire imaging data,such as gamma ray or photon imaging data. Prior to acquiring images, aradiopharmaceutical is usually taken orally or injected into an objectsuch as a patient. The radiopharmaceutical undergoes nuclear decay,emitting, either directly or indirectly through annihilation, gammaphotons at certain rates and with characteristic energies. One or moredetector units are placed around the object to record or monitoremissions. In many cases, for convenience of manufacturing and dataprocessing, the detectors are organized in planar shape, thereforeacquiring data in 2D matrix format, which are often referred to asprojections. Based on the recorded information including position,energy and counts of such detected events, an image of theradiopharmaceutical distribution can be reconstructed to study thefunction of certain parts of the object (e.g., body parts of a patient).

However, existing collimator and detector designs suffer from variousissues. For example, parallel-hole collimators are conventionallytightly coupled (or attached) to detectors in order to reduce cross-talkbetween sensing pixels in detectors, such that there is only onepossible photon path to any sensing pixel. Generally, longer aperturesof a collimator would benefit imaging resolution of the imaging systembut deteriorate its signal sensitivity. Therefore, a length of aperturesof a collimator has to be determined with a tradeoff between imagingresolution and signal sensitivity.

The present disclosure provides embodiments of collimator designs wherea collimator with non-uniformly distributed apertures is deployed in adistance away from a detector, such that some areas of the detector aresimultaneously illuminated by photons passing through more than oneaperture. Stated differently, at least some apertures of the collimatorhave their respective illuminating areas on the detector overlapped witheach other. By spacing a collimator from a detector and utilizing largeraperture size (or wider acceptance angle), effective length of aperturesof the collimator is increased resulting in improved imaging resolutionwithout sacrificing signal sensitivity. Also, in some embodiments of thepresent disclosure, apertures of a collimator have a repetitive pattern.In furtherance of the embodiments, the pattern may be one of a uniformlyredundant array (URA) pattern, a modified uniformly redundant array(MURA) pattern, a perfect binary array (PBA) pattern, a random pattern,a pseudo random pattern, and other suitable patterns. The repetitivepattern allows a radiation-based imaging system to adopt a simplifiedimage reconstruction algorithm to reduce computation complexity and toincrease system performance. In various embodiments, a collimator mayalso adopt a light-weight design by having a thin plate definingapertures without fully filling closed holes. Accordingly, the newcollimator designs improve performance of radiation-based imagingsystems from various aspects.

FIGS. 1A-1C illustrate an example radiation-based imaging system 100 (anuclear medicine imaging system in particular) that incorporatesfeatures of the present disclosure according to some embodiments. FIG.1A is a cross-sectional sideview of a portion of the system 100 in theX-Z plane. FIGS. 1B and 1C are axial views of the system 100 in the Y-Zplane in two embodiments. The imaging system 100 may be used tomedically examine or treat a target object such as a patient. Theimaging system 100 includes an integrated gantry 102 that furtherincludes rotating mechanism (e.g., a rotor oriented about a gantrycentral bore) that is configured to support and rotate one or moredetectors 108 (two detectors 108 in opposing positions are shown) aboutan axial axis (e.g., X-direction as shown). In one embodiment asillustrated in FIG. 1B, two detectors 108 are operable to rotate along acircle 152 in opposing positions with normal directions 154A and 154B tothe respective top surfaces of the two detectors 108 both pointing tothe center of the circle 152 and in opposite directions. In analternative embodiment as illustrated in FIG. 1C, two detectors 108 aresimilarly operable to rotate along the circle 152 in opposing positionswith the normal directions 154A and 154B to the respective top surfacesof the two detectors 108 pointing to the center of the circle 152 aswell. The difference is that the normal directions 154A and 154B in FIG.1B are not exactly opposite but form a small angel Y. The angel Y mayrange from about 0.5° to about 20° depending on system performanceneeds, in accordance with some embodiments. The details regarding thesetups in FIGS. 1B and 1C will be discussed later on. Each detector 108works in tandem with a collimator 110. The collimator 110 is a devicethat guides photon path. In molecular imaging, photons may originatefrom unknown locations inside a subject, unlike in X-ray or CT wherephotons are emitted from a known source (or sources) position. Withoutcollimators 110, photons from all directions may be recorded bydetectors 108, and image reconstruction may become difficult. Therefore,collimators 110 are deployed to guide photon paths so that images can bereconstructed. The imaging system 100 further includes a patient table112 coupled to a table support system 114, which may be coupled directlyto a floor or may be coupled to the gantry 102 through a base. Thepatient table 112 is configured to be able to slide with respect to thetable support system 114, which facilitates ingress and egress of apatient 150 into an examination position that is substantially alignedwith the axial axis. A control console 120 provides operation andcontrol of the imaging system 100, such as in any manner known in theart. For example, the control console 120 may be used by an operator ortechnician to control mechanical movements, such as rotating the rotor104, moving, rotating, or tilting the detectors 108 and collimators 110,and sliding the patient table 112. The imaging system 100 furtherincludes computer components (not shown), such as data storage units,image processors, image storage units, and displays, for acquiring dataand reconstructing nuclear medicine images. In some embodiments, one ormore computer components can be partially or entirely located at aremote location (e.g., using the cloud computing). In some embodiments,one or more of these components may exist locally or remotely.

In some embodiments, the detector 108 is a semiconductor detector, suchas one based on cadmium telluride (CdTe), cadmium zinc telluride (CZT),or high purity germanium (HPGe). In some embodiments, the detector 108is a scintillator (such as sodium iodide (NaI) or caesium iodide (CsI)based) detector. In some other embodiments, the detector 108 may also bea scintillator coupled with compact photo multiplier tubes (PMTs),silicon photomultiplier tubes (SiPMT), or avalanche photodiodes. One ormore radiopharmaceuticals orally taken or injected into patient 150undergo nuclear decay and may emit, either directly or indirectlythrough annihilation, radiation (e.g., gamma photons) at certain ratesand with characteristic energies. The detector 108 is placed nearpatient 150 to record or monitor emissions. Based on recordedinformation such as position, energy, and counts of such detectedevents, an image of radiopharmaceutical distribution may bereconstructed to study the status or function of certain body parts onpatient 150.

The collimator 110 includes plural walls (known also as septa) thatdefine one or more apertures (also referred to as openings orthrough-holes). In various embodiments, septa are made of heavy metalsuch as lead or tungsten. The thickness of the septa, depending on theenergy of photons, is large enough to stop the majority of the radiationso that the photons primarily pass through the small apertures on theplate. The thickness needs to be greater to image higher energy gammarays. The collimator 110 is placed between detector 108 and an imagingobject, such as the patient 150. The apertures of a collimator determinethe directions and angular span (acceptance angle) from which radiationcan pass through to reach certain position on the detector. Depending onnumber and geometrical placement of apertures, the collimator 110 may bea single-hole collimator, a multi-hole collimator, or a coded aperturecollimator, or other suitable type of collimator.

The imaging system 100 may include other necessary parts for an imaginggantry such as connectors that couple parts together (e.g., connectingdetector 108 and collimator 110 together), motors that cause parts tomove, photon shielding components, a housing component that containsother parts, etc. For example, a coupling and shielding component 116may connect detector 108 and collimator 110 such that both move (e.g.,rotate) together, and prevent radiation (photons) from reaching detector108 through paths other than collimator 110. In other embodiments,detector 108 and collimator 110 may move individually with respect toeach other.

FIG. 2A shows a perspective view of an example multi-hole (ormulti-aperture) collimator 202 and FIG. 2B shows a cross-sectional view(along B-B cut in FIG. 2A) of the collimator 202. The collimator 202 hasnumerous holes 208, each having a height H and a diameter (or width) W.The height H is also the thickness of the collimator 202. The holes 208are also referred to as apertures, openings, or through-holes. Theacceptance angle ⊖ of an aperture 208 is defined by the angle betweentwo rays R0 and R1 traveling from an edge point on the upper opening ofthe aperture 208 to an opposing edge point on the lower opening of theaperture 208. Only incident photons (or radiation) traveling within theacceptance angle ⊖ can pass through the aperture 208 (withoutconsidering a small portion of rays that may penetrate the septa 212).As discussed above, the septa 212 are made of radiation absorbing heavymetal(s) or alloy, such as lead or tungsten. The septa 212 absorbs mostradiation that do not emanate from (or travel at) the direction ofinterest. A collimator for higher energy radiation has much thickersepta than a collimator for lower energy radiation. The septa aregenerally designed so that septal penetration by unwanted photon doesnot exceed 5% and in some instances does not exceed 1%. It should benoted that radiation or photon blocked or absorbed by a collimator doesnot require a 100% blocking rate because a small percentage of photons(e.g., 5% or less) may still penetrate through the thickness of theradiation absorbing material. In other words, blocking (or other similarterms) means that vast majority of the photons (e.g., 95% or more, or99% or more) are absorbed by the radiation absorbing material.

The collimator 202 provides positional information for detected photonsby restricting the incident photon acceptance angle ⊖. Generally, thesmaller the acceptance angle ⊖, the higher the imaging resolutionprovided by the collimator 202. The collimator 202 may have a largenumber of substantially identical, long and narrow apertures 208 placedside by side and in parallel to each other. The long and narrowapertures come with small acceptance angle ⊖ and accordingly highimaging resolution. The collimator 202 may have a thickness H largerthan 15 mm, such as 20 mm to 70 mm, with an aperture diameter (or width)W around 1 mm to 5 mm, thereby providing a large aspect ratio (H/W) andsmall acceptance angle ⊖. The acceptance angle ⊖ of the parallel-holecollimator 202 is limited to a small angle, such as not greater than15°. If the acceptance angle ⊖ is too large (such as greater than 15°),the imaging resolution provided by the particular parallel-holecollimator is considered undesirably low. Unless otherwise specified,the acceptance angle ⊖ of the example collimators in the presentdisclosure is not greater than 15°. In addition to the holes in FIG. 2Bthat are rectangular in the “x-z” cross-section, the concept ofacceptance angle can be extended to holes in other forms, such as holesin converging or diverging collimator, where the holes can be oftrapezoidal shape and may be slanted, representing the largest angledifference of rays that may pass through the hole.

The collimator 202 illustrated in FIG. 2A is a parallel-hole collimatorwith uniformly distributed apertures. In the illustrated embodiment, theapertures 208 are substantially identical, each having the same height Hand the same diameter or width W, except for variations caused byfabrication precision limitations. Accordingly, each aperture has thesame acceptance angle ⊖ that is small (such as not larger than 15°, suchas about 5° in a particular example). The aperture pitch P is alsosubstantially the same on the collimator 202. In other words, theaperture spacing S (septa thickness) is uniform on the collimator 202.Herein, apertures with uniform aperture shape, aperture size, aperturelength, and aperture pitch are termed as “uniformly distributedapertures.”

FIGS. 2C and 2D illustrate top views of two arrangements ofparallel-hole collimators (such as the collimator 202) with uniformlydistributed apertures, while other arrangements are possible and do notdepart from the spirit and scope of the present disclosure. In FIG. 2C,apertures 208 are arranged in orthogonal rows and columns to form anorthogonal two-dimensional grid arrangement. Each aperture 208 can beregarded as being aligned with a unit grid 240 of a square shape in agrid network (represented by dashed lines in FIG. 2C). Two adjacentapertures 208 have the same pitch P, where P=W+S, W is the width (ordiameter) of the aperture 208 and S is the minimum spacing (or septathickness) between two adjacent apertures 208. In FIG. 2D, apertures 208are arranged in a staggered fashion with a succession of rows adjacentto each other and two adjacent rows being offset from each other by adistance (or an offset). The offset may be W in an embodiment or othersuitable values in alternative embodiments. Each aperture 208 can beregarded as being aligned with a unit grid 240 of a hexagonal shape in agrid network (represented by dashed lines in FIG. 2D). Two adjacentapertures have the same pitch P, where P=W+S, W is the width (ordiameter) of the aperture 208 and S is the minimum spacing (or septathickness) between two adjacent apertures 208. In some alternativeembodiments (not shown), apertures 208 may be aligned with a unit grid240 of a honeycomb shape of a grid network. FIGS. 2E and 2F illustratevariations of FIGS. 2C and 2D, respectively. One or more of the unitgrids 240 may be designed to have no aperture(s) there-through, which isequivalent to having an aperture (represented by a dashed circle inFIGS. 2E and 2F) that is filled up (or closed) by the septa material.Such aperture arrangement is considered as having a varying aperturepitch or having closed holes, and thus not in the category ofparallel-hole collimators with uniformly distributed apertures. In otherwords, the apertures in FIGS. 2E and 2F are non-uniformly distributed.

FIG. 3 is a schematic cross-sectional view of a collimator 202 asillustrated in FIG. 2B and a detector 204 that work in tandem togenerate images that represent radiopharmaceutical distributions withina target object 206 (e.g., a patient). The collimator 202 is positionedbetween the target object 206 and the detector 204 and configured tofilter radiation by blocking certain photons and passing through otherphotons. In the illustrated embodiment, coupling and shieldingcomponents connecting the collimator 202 and the detector 204 areomitted for the sake of simplicity. In the present embodiment, thecollimator 202 is a parallel-hole collimator where the apertures orholes in the collimator 202 have a rectangular cross-section and arearranged parallel to each other. In alternative embodiments, theapertures or holes in the collimator 202 may have a divergingcross-section, a converging cross-section, or some other cross-sectionalshape.

The detector 204 includes an array of sensing pixels 214, such as arectangular array, a square array, or other suitable arrays of pixels214. In operation, each sensing pixel 214 records or monitorsindividually the amount of radiation incident thereon and generatessignals (e.g., voltage or current) in association with the amount ofradiation. The sensing pixels 214 may be of substantially the same sizeand the same shape (e.g., circular, rectangular, or square shape). Thesize of the sensing pixels 214 may range from about 1×1 mm² to about 5×5mm² in various embodiments. The sensing pixel pitch P′ of the array mayrange from less than 1 mm to about 6 mm in various embodiments. In anexample, a CZT or silicon multiplier (SiPM) based detector 204 can befabricated in a size of 4 cm×4 cm, consisting of an array of 16×16sensing pixels with a unit pixel size of 2.5 mm×2.5 mm. In someembodiments, the detector 204 includes appropriate electronic circuits(e.g., ASICs) to collect and process the signals generated from thesensing pixels 214. In some other embodiment, the sensing pixels 214 arenot physically distinctive from each other and are mere results ofdigitization of a continuous detector surface, as in the case of mostPMT-based detector systems. For example, the detector surface may bedigitized as a grid network that is same as the grid network in thecollimator 202 with each unit grid in the detector surface correspondingto an aperture in the collimator 202.

In FIG. 3 , for simplicity, assume that the sensing pixel pitch Vsubstantially equals the aperture pitch P, such that each sensing pixel214 is directly under a corresponding aperture 208. Further, thecollimator 202 is tightly coupled (or attached) to the detector 204 withminimal spacing between the collimator 202 and the detector 204 suchthat photons are allowed to only travel along the apertures 208 to reachcorresponding sensing pixel 214 immediately under it, although minimalor negligible cross-talk is possible (e.g., photons may pass through thesepta or photons may pass through one aperture but hit a sensing pixeldirectly under another, different, aperture). In the present disclosure,the terms “tightly coupled to” and “attached to” both refer to a spacingbetween a collimator and a detector being less than half of a thicknessof the collimator including the instance where the collimator 202 andthe detector 204 are in physical contact.

For a parallel-hole collimator, its imaging resolution degrades quicklywhen the imaging source moves away from the collimator. For a collimatorwith an aperture size W and length (or effective length) of H_(e), for atarget object 206 located at a vertical distance Z above the collimatortop surface 210, the imaging resolution of the collimator, R_(c), isgiven by equation (1) below:R _(c)=(H _(e) +Z)/H _(e) *W=(1+Z/H _(e))*W.  (1)The effective aperture length H_(e) is given by H_(e)=H−2/μ where H isthe aperture length and μ is a linear attenuation coefficient of thecollimator material. For lead, at 150 keV, μ=22.43 cm⁻¹, and 2/μ≈1 mm.The aperture length H is usually greater than 20 mm, therefore H≈H_(e).For the sake of simplicity, H and H_(e) are used interchangeably hereinunless they have a meaningful difference. As a simple way to look at Eq.(1), the imaging resolution R_(c) equals to an area at a distance Z thatcan be seen through an aperture from the bottom of the aperture, asshown in FIG. 3 .

As seen from Eq. (1), the imaging resolution R_(c) increases linearlywith distance Z. And at the same distance Z, R_(c) is smaller (i.e.,having a better imaging resolution) if H_(e) is bigger, meaning that theimaging resolution would be improved for longer apertures (i.e., largerH). However, longer apertures adversely affect signal sensitivity in aninverse-square relation. Let G denote the collimator efficiency, definedby the ratio of the amount of radiation rays (e.g., gamma rays) passingthrough the collimator to the amount of the radiation rays emitted bythe source, then G is in direct proportion to H_(e) ⁻² (i.e., G∝H_(e)⁻²). Hence aperture length H has to be chosen to balance imagingresolution and signal sensitivity.

FIG. 4 illustrates an alternative collimator design termed as a “spreadfield imaging (SFI) collimator”, which provides an increased equivalentaperture length, therefore higher imaging resolution, withoutsacrificing signal sensitivity. In comparison to the parallel-holecollimator 202 as shown in FIG. 3 , the SFI collimator 203 as shown inFIG. 4 has at least two distinctive features. First, the spacing Dbetween the SFI collimator 203 and the detector 204 is significantlyincreased compared with the configuration in FIG. 3 . Second, theapertures 208 of the SFI collimator 203 are not all identical and differin at least one aspect. These are further discussed below.

The spacing D between the SFI collimator 203 and the detector 204 isincreased to allow photons passing through one aperture 208 to beincident on an area of the detector 204 that extends beyond the aperture208. In other words, radiations from the target object 206 travelthrough an aperture 208 and spread and illuminate an area on thedetector 204 that is substantially larger than the size of the aperture208 and extends to areas that are directly underneath other neighboringapertures. In contrast, when the collimator 202 is tightly coupled tothe detector 204 such as shown in FIG. 3 , radiations from a targetobject 206 that travel through one aperture 208 only illuminate an areaon the detector 204 that substantially equals the size of the aperture208. As illustrated in FIG. 4 , an incoming photon incident betweenlines A1 and A2 that define acceptance angel ⊖ would travel through theaperture 208 and arrive at the detector 204 and “illuminate” thedetector 204. The surface area of the detector 204 bounded by linesdefining acceptance angel ⊖ of an aperture 208 is denoted as theilluminating area of the respective aperture 208. For example, theilluminating area of the center aperture 208 is defined by a surfacearea of the detector 204 between the lines A1 and A2 that intersect thedetector 204. An illuminating area's size and shape depend on thecorresponding aperture's profile and the spacing D between thecollimator 202 and the detector 204. In some embodiments, anilluminating area of an aperture 208 on the detector 204 is at leasttwice the size of the corresponding unit grid which includes thecorresponding aperture 208 and half of the septa surrounding thecorresponding aperture 208 (note that the boundary of a unit grid liesin the middle of septa between the unit grid and neighboring unitgrids). Further, an illuminating area of one aperture 208 may overlapwith illuminating areas of its neighboring apertures. For example, morethan 10%, more than 20%, or even 50% (considering only radiation thatpass through the aperture 208 and excluding radiation that penetrate thesepta surrounding the aperture 208) of an illuminating area may beoverlapped with other illuminating areas in various embodiments. FIG. 4illustrates an overlapping area between the illuminating area defined bylines A1 and A2 under the aperture 208 and another illuminating areadefined by lines A1′ and A2′ under a neighboring aperture. In otherwords, a point (or a sensing pixel 214) in the overlapping area of thedetector 204 may receive radiations from more than one aperture 208.Furthermore, in some embodiments, any sensing pixel 214 in the detector204 is simultaneously illuminated by no more than a percentage of thenumber of the apertures 208, wherein the percentage is less than about25%. In some embodiments, the percentage is less than 10%, less than 5%,or even less than 2%. In some other embodiments, the illuminating areaof any aperture is no more than a percentage of the total illuminatingarea (by all holes) of the coupled detector 204, wherein the percentageis less than 10%, less than 5%, or even less than 2%. In comparison,holes in coded aperture or multi-pinhole collimators generallyilluminate a larger percentage of total illuminating areas than theembodiments of the present disclosure. For example, the illuminatingarea of a hole in those collimators may be greater than 25% or evengreater than 40% of the total illuminating area of all holes in therespective collimator, which introduces large amount of cross-talk tothe imaging system. By limiting the illuminating area of any hole to beno more than 10%, 5%, or even 2% (depending on system performance needs)of the total illuminated area (by all holes) of the coupled detector,cross-talk from different apertures is effectively reduced and hencegood performance on the imaging resolution and signal sensitivity can beachieved.

Shielding 244 (usually with heavy metal materials) is provided along theperipheral region to cover (or seal) the space between the collimator203 and the detector 204 to prevent radiation reaching the detector 204through that space. Notably, although FIG. 4 shows gaps between theshielding 244 and the SFI collimator 203 and between the shielding 244and the detector 204, it is for illustration purpose only. In variousembodiments, shielding 244 is deployed to provide a closed (or sealed)area such that only radiations through the collimator 203 can arrive atthe detector 204.

In the present embodiment, the apertures 208 of the SFI collimator 203are not all identical. They may differ in aperture shape, aperture size,or even aperture length. If aperture sizes are different, the acceptanceangle ⊖ may vary, but the largest acceptance angle ⊖ remains not greaterthan 15° in the present embodiment. As discussed above, an acceptanceangle ⊖ not greater than 15° provides a desirable imaging resolution.Also, for a given collimator thickness H, smaller acceptance angle ⊖translates to smaller aperture size, and consequently smaller collimatordimensions. An acceptance angle ⊖ not greater than 15° provides a goodcompromise between a compact collimator design and manufacturingdifficulties (e.g., mechanical tolerance). Further, an acceptance angle⊖ greater than 15° increases cross-talk from adjacent apertures andresults in deteriorated resolution and increased complexities in postimaging processing. In some applications, an acceptance angle ⊖ can beless than about 10°, or even less than about 5°, in order to achieve ahigher imaging resolution and less cross-talk based on systemperformance needs. In some embodiments, some of the apertures 208 of theSFI collimator 203 may be closed, meaning substantially blocked and notallowing photons to pass through. Accordingly, aperture pitch may alsovary across the collimator 203. For example, in FIG. 5B, the pitch andseptum around 208′ is relatively different than other septa. Suchapertures with non-uniformity in at least one parameter of apertureprofiles (e.g., aperture shape, aperture size, aperture length, andaperture pitch) are referred to as “non-uniformly distributedapertures.” FIG. 5A illustrates an embodiment of an SFI collimator 203with different aperture shapes (e.g., circle and square), differentaperture sizes, and different aperture pitches (due to blocked aperturesrepresented by dashed circles). In FIG. 5A, each aperture 208 alignswith the respective unit grid 240 (e.g., center-to-center alignment).FIG. 5B illustrates yet another embodiment of an SFI collimator 203, inwhich there is at least one aperture 208′ offset from its respectiveunit grid 240. The SFI collimator 203 with such aperture arrangement isalso regarded as a parallel-hole collimator with non-uniformlydistributed apertures. It is noted that FIGS. 5A and 5B merely show aportion of an SFI collimator 203. In an embodiment, the total number ofapertures 208 on the collimator 203 exceeds one thousand (1,000), suchas about two thousand (2000), five thousand (5000), ten thousand(10,000), thirty thousand (30,000), and even one hundred thousand(100,000). The large number of apertures are beneficial for highersensitivity, good coverage of field of view (FOV), and better use ofdetector area because each aperture only illuminates a small percentageof the surface area of the detector 204 and there is significantcross-talk or multiplexing between apertures 208.

In some embodiments, a portion or all of the apertures 208 in thecollimator 203 can be arranged in repetitive patterns, such as arepetition of patterns of size 3×3, 4×4, 3×5, 5×5, etc. The repetitivepattern is referred to as a basic pattern. In some embodiments, thebasic pattern has odd number of rows and/columns such that there is onecentral hole in the basic pattern, which can be advantageous inprocessing data. FIG. 6A illustrates a top view (or a portion of a topview) of an embodiment of the SFI collimator 203. At least a portion ofthe SFI collimator 203 includes a repetition of a basic pattern of 5×5unit grids, with one basic pattern illustrated in FIG. 6B where whitepixels represent open apertures and grey pixels represent closedapertures. The open apertures are surrounded by septa. The dotted linesin FIG. 6A represent the boundaries among the basic patterns. In theillustrated embodiment, an aperture aligns with a unit grid of squareshape and may expand to the size of the whole unit grid. The basicpattern can be a coded aperture pattern, such as a URA, a MURA, a PBA, arandom or pseudo random pattern. In some embodiments, the number ofrepetitive patterns is more than 2×2, such as 3×3, 3×5, 5×5, etc. InFIG. 6A, the illustrated basic pattern is a MURA 5 pattern and isrepeated 3 times in X-direction and 3 times in Y-direction in forming acollimator (or a portion of a collimator) of a size 15×15. In variousembodiments, a basic pattern can be repeated in X-direction andY-direction any times, respectively, to fit a need of systemrequirement. FIG. 6C illustrates a top view of another embodiment of anSFI collimator 203 (or a portion thereof) where a basic pattern of MURA5 is repeated 25 times in X-direction and 25 times in Y-direction informing a collimator (or a portion of a collimator) of a size 125×125.In the illustrated embodiments, shape and size of the apertures areidentical. In some embodiments, the apertures can be different in shape,in size, or both.

Referring back to FIG. 4 , the spacing D between the collimator 203 andthe detector 204 can be chosen such that the illuminating area of eachaperture 208 on the detector 204 is the same as or no greater than arepetitive basic pattern but greater than at least twice of the aperturespacing (pitch). The size of an illuminating area of an aperture 208 onthe detector 204 substantially equals to the size of a basic pattern ofthe collimator 203, such as illustrated by the dotted lines B1 and B2 inFIG. 4 . As will be discussed in further details below, having the sizeof an illuminating area substantially equal to (or being an integermultiple of) a basic pattern provides a fast image reconstructionalgorithm that significantly increases system efficiency and accuracy.As a result, the spacing D between the collimator 203 and the detector204 is optimized when it is greater than half of the aperture length(collimator thickness) H. In various embodiments, D may be less than 10times of H, for example between 1.5 and 10 times of H, between 1 and 7times of H, between 1.5 and 7 times of H, or some other suitable range.If D is too small, such as less than 1.5 times H, the effect onresolution improvement is not significant. On the other hand, if D islarger than 10 times of H, cross-talk from neighboring apertures wouldbe high and cause increased complexity and resolution degradation duringimage reconstruction. In some examples, D is about 1 time, 1.5 times, 2times, 2.5 times, 3 times, or 3.5 times of H.

Still referring to FIG. 4 , for a sensing pixel 214 of the detector 204,the area that can be seen through an aperture directly above it, alsoreferred to as the imaging resolution R_(n), is given by Eq. (2) below:R _(n)=(H+D+Z)/(H+D)*W.  (2)Note that the difference between Eq. (1) and Eq. (2) is that H_(e) inEq. (1) is replaced by (H+D) in Eq. (2), essentially extending theaperture length by D, therefore allows the imaging resolution to besignificantly improved. R_(n) can be smaller than R_(c) even if aperturesize, W, is increased for higher signal sensitivity.

The fact that photons may pass through one aperture and then hit adetector area directly underneath another aperture means there iscross-talk or multiplexing. In comparison, for any sensing pixel on thedetector surface when a parallel-hole collimator (e.g., the collimator202 as shown in FIG. 3 ) is equipped, there is only one aperture thatphoton can pass through and reach it (excluding septa penetration whichis an effect to be suppressed in parallel-hole collimator design). Thiscross-talk effect usually degrades resolution because there are multiplepossible paths for a photon detected at a detector location, and for asource at a certain point there are multiple apertures the radiationrays may pass through to reach the detector. And this is the case if allapertures are essentially identical as in a parallel-hole collimator.

On the other hand, regarding the SFI collimator 203 as shown in FIG. 4 ,the apertures are not all identical. More specifically, the apertureswithin the visible area of a sensing pixel on the detector surface arenot all identical (the visible area here means the congregates of allapertures that a photon may pass through to reach that sensing pixel onthe detector surface). As a result, sources close to each other willproject different shadows on the detector because the aperture patternsbelow them are different. These differences help the reconstructionalgorithm to recover the original source distribution, i.e., the objectimage, at a high resolution similar to R_(n). The detector surfaces areusually digitized as a network of grids, and each grid represents aboundary of a sensing pixel. In some embodiments, the aperture patternsseen by neighboring sensing pixels are different.

Similar to SPECT imaging, images (also referred to as projections) canbe acquired from multiple angles by rotating the set of coupledcollimator (such as the collimator 203) and detector (such as thedetector 204) around a target object. In this acquisition mode, thecoupled collimator and detector are moving together with no relativemotion between them. A forward projection p at a certain angle α can bewritten as{circumflex over (p)} _(α)(i)=Σjf(j)Kα(i,j)  (3)where i and j are indices of detector pixel and object image voxel, f(j)is the value of voxel object j, and Kα(i,j) is the probability of aphoton emitted from voxel j being detected at pixel i when the camera isat angle α. To reconstruct the original object image f, a method to useis an MLEM algorithm where f can be found iteratively

$\begin{matrix}{f_{j}^{({k + 1})} = {\frac{{\hat{f}}_{j}^{(k)}}{\sum\limits_{i = 1}^{J}K_{ij}}{\sum\limits_{i = 1}^{I}\frac{p_{i}K_{ij}}{\sum\limits_{j = 1}^{J}{K_{ij}{\hat{f}}_{j}^{(k)}}}}}} & (4)\end{matrix}$ $\begin{matrix}{or} & \end{matrix}$ $\begin{matrix}{{f^{({k + 1})}(j)} = {\frac{f^{(k)}(j)}{\sum\limits_{i,\alpha}{K{\alpha\left( {i,j} \right)}}}{\sum\limits_{i,\alpha}\frac{{p\left( {i,\alpha} \right)}K{\alpha\left( {i,j} \right)}}{\sum\limits_{j}{K{\alpha\left( {i,j} \right)}{f^{(k)}(j)}}}}}} & (5)\end{matrix}$where f^((k))(j) is the object image at k^(th) iteration, and p(i, α) isthe measured projection at detector pixel i and angle α. This algorithmhas three steps—forward projection, calculating ratio, andback-projection. A variation of this algorithm is called OSEM, where theprojections are divided into N subsets, and computation starts withseveral iterations using one subset of projections, and moves onto thenext subset until all subsets have been computed. The process may repeatwith different subset divisions and different number of iterations foreach subset.

The algorithm as shown in Eq. (5) is extremely time consuming andrequires enormous storage for the K matrix considering the large numberof voxels and pixels, multiplied by the number of angles. The projectionat one angle can be digitized as from 64×64 to up to 512×512 pixels, andusually acquisition from 60 or 120 angles is needed. And the objectimage often has 128×128×128 or 256×256×256 voxels. Therefore the matrixKα(i,j) is extremely large.

When the apertures are made up of repetitive basic patterns and therespective through holes in all repetitive patterns have the same shapeand dimensions (even though the holes may differ in the basic pattern),the matrix K and the algorithm can be simplified. Generally, for arepetitive basic pattern of a size X×Y (X and Y can be different), thereis only a number of patterns that equals a multiple of the product ofX×Y that a point source may project on the detector. Shown in FIG. 6A orFIG. 6B is an example where the repetitive pattern is a 5×5 (X=Y=5) MURA5 pattern. Let m be the index of holes (grid units, including open andclosed holes) in the basic pattern, m=1, . . . 25. In this example,consider a plane located at distance Z from the collimator 203 (see FIG.4 ), a point source at any point on that plane projects a pattern on thedetector 204, where the size of projected pattern is much smaller thanthe size of detector, and there are only X×Y=25 patterns a point sourcemay project on the detector, depending on the index of the apertureright below it (except in border region), denoted as psf_(m,Z)(x,y)where x=−M, . . . M and y=−N, . . . , N. Here the detector pixel size isthe same as the collimator pitch (hole inter-spacing) or a fraction ofthat. Therefore, the 25 patterns can be indexed by the aperture in thebasic 5×5 pattern. In the meantime, the object image at distance Z,denoted as f_(Z), whose pixel (also called voxel) size is the same asthe collimator pitch (hole inter-spacing) and the pixels are alignedwith the collimator pitch, can be divided into 25 sub-images of the samesize as f_(Z), where in each sub-image the pixels on top of the apertureof the same index are kept the same, and the rest of the pixels are setto 0, as illustrated in FIG. 7 . Let m be the pattern index, then aslice of object image at distance Z, f_(Z), can be denoted bysub-images, f_(Z)(j, m), given by

$\begin{matrix}{{f_{z}\left( {j,m} \right)} = \left\{ {\begin{matrix}{f_{z}(j)} & {j{is}{on}{top}{of}a{hole}{with}{index}m} \\0 & {otherwise}\end{matrix}.} \right.} & (6)\end{matrix}$This way the forward projection step for object image at Z in Equation(5) can be rewritten as{circumflex over (p)} _(α)(Z)=Σ_(j) Kα(i,j)f _(z,α) ^((k))(j)=Σ_(m) f_(z,α) ^((k))(j,m)*psf _(m,Z)  (7)where {circumflex over (p)}_(α)(Z) is the forward projection calculatedbased current estimate of object image f_(Z) ^((k)), and * representsconvolution. Similar approach can be taken to compute theback-projection step. It is known that convolution is computationallymore efficient than matrix multiplication using FFT algorithms. Thisidea can be extended to voxel sizes as a fraction of collimator pitch,where a multiple of X×Y convolutions of psf patterns and correspondingsub-images can be used. For example, if a voxel size is half ofcollimator pitch, 4 (2×2) times of 25 convolutions (i.e., a total of 100convolutions) of psf patterns and corresponding sub-images can be used.This approach may bring higher accuracy with increased computationalcomplexity.

Eq. (7) also indicates that if object image is organized in slicesparallel to collimator surface denoted by distance Z, then theprojection pattern psf_(m,z) is the same for different angle α. Thisfurther simplifies the algorithm.

One way is to implement Eq. (5) for each angle independently, taking aout of the summation; then take summation of estimate f_(Z)(j) alongdistance Z to obtain a secondary projection at that angle, p′_(α). Sincethe projection geometry to derive p′_(α) from object image f is similarto parallel hole collimation, algorithms for parallel hole collimationimage reconstruction can be used to reconstruct f from p′_(α), such asfiltered back-projection (FBP), algebraic reconstruction technique(ART), and OSEM methods.

An alternative is to convert f_(Z) to f_(α,z) at the beginning of eachiteration through interpolation, where f_(a,z) consists of slices(marked by Z) parallel to collimator surface at that angle. Thenprojection-back-projection steps can be executed before applyinginterpolation to convert the back-projected ratio, q_(a,z), given by

$\begin{matrix}{{q_{\alpha,Z} = {\sum\limits_{i}\frac{{p\left( {i,\alpha} \right)}K{\alpha\left( {i,j} \right)}}{\sum\limits_{j,Z}{K{\alpha\left( {i,j} \right)}{f_{\alpha,Z}^{(k)}(j)}}}}},} & (8)\end{matrix}$to original grid in f, and then calculate the updating ratio for f_(Z).

Referring back to FIG. 4 , regarding the collimator 203, the height H ofan aperture (i.e., the thickness of the collimator 203) is sometimesmuch larger than its opening width or diameter W. For example, anaperture width W may be less than 2 mm, while an aperture height H maybe greater than 20 mm. However, for closed apertures, the apertures donot need to be fully filled, but rather to be filled with enoughthickness to block radiation to pass through that hole. For example,when a radioisotope Tc-99m is used for material of septa, lead of 3 mmthickness may block more than 99% of incident radiation at 140 keV gammarays. Hence the collimator may be fabricated in a light-weight form.Referring to FIGS. 8A and 8B, the collimator 203 is a collimator withopen and closed holes and includes two sections. One section is similarto a parallel-hole collimator with uniformly distributed through-holes(also referred to as a parallel-hole section 262). The other section issubstantially a thinner plate 264 (with thickness enough tosubstantially block radiation) with non-uniformly distributedthrough-holes, such as with less through-holes than those in theparallel-hole section 262 (e.g., approximately half of through-holes).The collimator 203 shown in FIGS. 8A and 8B is also referred to asmulti-section collimator. The through-holes in the thin plate 264 arealigned with the through-holes in the parallel-hole section 262 tojointly define aperture pattern of the collimator 203, while otherthrough-holes in the parallel-hole section 262 are blocked by the opaquematerial of the thin plate 264. Therefore, the through-holes in the thinplate 264 define the positions of the final apertures of the collimator203. The thin plate 264 is also referred to as a patterned-aperturesection 264. In some embodiments, all through-holes in the parallel-holesection 262 are substantially identical, while through-holes in thepatterned-aperture section 264 may be different, even including closedones. Further, the patterned-aperture section 264 may be moveable insome embodiments, such as operable to slide horizontally with respect toa surface of the parallel-hole section 262. Thus, multiple projectioncan be acquired at one angle by moving the patterned-aperture section264 with respect to the parallel-hole section 262.

The patterned-aperture section 264 has a thickness H1 that issufficiently thick to block targeted radiation. In various embodiments,a thickness H2 of the parallel-hole section 262 may be about 2 to about10 times of the thickness H1 of the coded-aperture section 264. Forexample, an aperture length of 25 mm may be constructed with aparallel-hole section 262 having a thickness of 20 mm and apatterned-aperture section 264 having a thickness of 5 mm. In this way,the overall collimator weight can be significantly reduced compared withfully filled closed apertures. The patterned-aperture section 264 may beat one side of the parallel-hole section that faces the detector (FIG.8A) or faces the target object (FIG. 8B), or even in the middle of twosub parallel-hole sections (e.g., sub parallel-hole sections 262-a and262-b in FIG. 8C, where H2-a+H2-b=H2). In fact, the closed aperturesonly need a thin layer of heavy metal material to block radiation. Thisthin layer may even be broken up into multiple segments as needed. Hencethis new design may start by fabricating regular parallel through-holes,then a thin layer may be placed anywhere inside the open though-holes tomake closed apertures.

Although apertures illustrated in FIGS. 8A-8C have the samecross-section and opening width, many different designs exist to allowfor different aperture profiles. For example, the light weight designcan also be applied to collimators having apertures with the same pitch,but with different aperture size and septa. Some of such examples areillustrated in FIGS. 9A-9C. In FIG. 9A, the collimator 203 has someapertures with a diameter (or width) W and some apertures with a smallerdiameter (or width) W′. Instead of using septa of constant widththroughout the thickness of the collimator 203 for sidewalls of thenarrower apertures, septa may have thicker portions merely at lateralends. The thicknesses H1-a and H1-b at lateral ends are sufficient toblock targeted radiation and maintain the same smaller acceptance angle⊖ of what a narrower aperture designed to have. The spirit of themulti-part design above with reference to FIGS. 8A-8C can also beapplied to the example collimator in FIG. 9A. FIG. 9B illustrates such acollimator 203 with one parallel-hole section 262 and two patternedaperture sections 264-a/264-b that define aperture sizes. In some cases,only one of 264-a/264-b is needed to adjust the acceptance angle ⊖.Also, the apertures may have different shapes, both in cross-section andvertical section. The apertures may have different orientations in someembodiments. The patterned-aperture sections 264-a/264-b may defineaperture sizes together with open and closed apertures patterns, such asshown in FIG. 9C. Referring to FIGS. 8A-9C collectively, oneparallel-hole section 262 may be paired with differentpatterned-aperture sections 264 a and/or 264 b to create differentcollimators configurations. Therefore, multi-section collimatorsaccording to the present disclosure also provides a low-cost solutionbesides achieving light-weight designs. Notably, FIGS. 8A-C and 9A-Cdepict embodiments where adjacent sections of the multi-sectioncollimator are in physical contact with each other. In alternativeembodiment, the adjacent sections are tightly coupled to each other (toprevent photons from entering through one hole but exiting from another)without in physical contact as long as the collimator performance isassured.

Reference is now made to FIG. 10A. Unlike the exemplary collimatorsillustrated in FIGS. 8A-9C in which the parallel-hole section 262 andthe patterned-aperture section 264 are attached to each other, theexemplary collimators as shown in FIG. 10A has the parallel-hole section262 spaced from the patterned-aperture section 264. Further, thepattern-aperture section 264 may be tightly coupled to the detector 204.In the illustrated embodiment, a sensing pixel 214 of the detector 204has a corresponding aperture in the patterned-aperture section 264 toreceive illumination from the parallel holes further above in theparallel-hole section 262. The apertures in the patterned-aperturesection 264 intentionally differ in sizes, resulting in differentnumbers of parallel holes in the parallel-hole section 262 that thepixels 214 can be illuminated. For example, a sensing pixel 214 a has alarger corresponding aperture in the patterned-aperture section 264 thana neighboring sensing pixel 214 b. As a result, the sensing pixel 214 acan be illuminated by multiple parallel-holes in the parallel-holesection 262 bounded between the lines C1 and C2 intersecting the bottomsurface of the parallel-hole section 262. As a comparison, due to asmaller corresponding aperture in the patterned-aperture section 264,the pixel 214 b can only be illuminated by a single parallel hole thatis directly above in the parallel-hole section 262 bounded by the linesD1 and D2 intersecting the bottom surface of the parallel-hole section262. The number of parallel holes in the parallel-hole section 262 thatcan illuminate the same sensing pixel 214 depends on the acceptanceangle of the corresponding aperture in the patterned-aperture section264. The number of parallel holes in the parallel-hole section 262 thatcan illuminate the same sensing pixel 214 also depends on the distanceH3 between the parallel-hole section 262 and the patterned-aperturesection 264. The distance H3 is selected based on a need of the systemperformance. A general rule is to have a distance H3 allowing some ofthe pixels 214 of the detector 204 to be illuminated by at least two ormore of the parallel holes 208 above. Notably, in an alternativeembodiment as shown in FIG. 10B, it may be the parallel-hole section 262that is tightly coupled to the detector 204, while thepatterned-aperture section 264 is spaced apart from the parallel-holesection 262.

The design presented in this invention can be adapted to othervariations with large number of long, narrow holes such as converging ordiverging holes collimators, modified with the two features presentedearlier.

Referring back to FIGS. 1A-1C, the radiation-based imaging system 100may employ at least two different sets of coupled collimator anddetector. In one of such embodiments, one set is with the SFI(spread-field imaging) collimator 203 (e.g., as shown in FIG. 4, 6A-C,8A-C, 9A-C, or 10A-B) that is spaced from the coupled detector and theother with parallel-hole collimator 202 (e.g., as shown in FIG. 3 ) thatis attached to the coupled detector. Usually in this configuration, theaperture opening (and/or acceptance angle) in the parallel-holecollimator 202 is smaller than the ones in the SFI collimator 203. Asshown in Eq. (1), parallel-hole collimator generally offers goodresolution at close range (small Z) because of smaller aperture opening,but its imaging resolution degrades quickly as the target object movesfarther away from the collimator. In contrast, the SFI collimator 203offers superior imaging resolution when the target object is fartheraway from the collimator. During a multi-angle image acquisition, thetwo sets of coupled collimator and detector module rotate around atarget object to acquire images (projections). Naturally a certain partof the target object is close to one collimator at some angles andfarther away at the opposite angle except for parts near the center ofrotation (COR). By combining these two collimators, one may assign moreweights to updating factors estimated from the parallel-hole collimator202 projections for locations closer to the parallel-hole collimator202, while more weights to updating factors estimated from the SFIcollimator 203 projections for locations farther away from theparallel-hole collimator 202. State differently, the weighing betweenestimations of the two sets of coupled collimator and detector modulesis distance-dependent. Another advantage of this configuration is that aquick estimate of object image can be obtained by reconstruction usingthe parallel hole projection alone and it can be used as initialestimate for the iterative reconstruction using projections from bothcollimators. There are several methods of choice to reconstructmulti-angle parallel hole projections, such as filtered back-projection(FBP), algebraic reconstruction technique (ART), and ordered subsetexpectation and maximization (OSEM). And the step may be carried out toreconstruct image at lower resolution (by applying low-pass filtering(LPF) on the projections, and/or reconstructed for larger pixels) toalleviate the lower counts due to the fact that parallel hole collimatorprojections here account for only half of angles of acquisition comparedto conventional scan with dual camera both with parallel holecollimators. In another embodiment, the system employs at least two setsof coupled collimator and detector modules that both include an SFIcollimator 203 (e.g., as shown in FIG. 4, 6A-C, 8A-C, 9A-C, or 10A-B)spaced from the coupled detector. But the long narrow through holes inthe two collimators are with different acceptance angles. For example,the largest acceptance angle of one SFI collimator 203 is at least twiceof the other SFI collimator 203, such as one for 10° and one for 5°. Inanother embodiment, the system employs at least two sets of coupledcollimator and detector modules, at least one detector is coupled withan SFI collimator 203 (e.g., as shown in FIG. 4, 6A-C, 8A-C, 9A-C, or10A-B) with long narrow holes (small acceptance angle) that is spacedfrom the coupled detector and another coupled with a multiple pinholecollimator, including coded aperture collimator where the largestaperture acceptance angle is substantially larger than those of the SFIcollimator 203, such as more than 20°.

Referring to FIG. 1B, if the radiation-based imaging system 100 employstwo identical sets of coupled collimator and detector in opposingpositions, each set of coupled collimator and detector may only need torotate half circle at equal sweeping steps. By combining data from thefirst and second half circles, the images from the full circle areacquired. For example, at a sweeping step of 3°, the first set mayacquire images at angles 0°, 3°, 6°, . . . , 177° in sequence; thesecond set may acquire images at angles 180°, 183°, 186°, . . . , 357°in sequence. If the radiation-based imaging system 100 employs twodifferent sets of coupled collimator and detector, since each set “sees”differently, each set needs to rotate a full circle. To maintain thesame operating time, each set may sweep the full circle at twice thesweeping steps. For example, at a sweeping step of 6°, the first set mayacquire images at angles 0°, 6°, 12°, . . . , 180°, 186°, . . . , 354°in sequence; the second set may acquire images at angles 180°, 186°,192°, . . . , 354°, 0°, . . . , 174° in sequence. For each given angleswept by the system, two images will be acquired, one from the first setand another from the second set. State differently, although the twosets “see” differently, but each set repeats acquiring image from thesame angle the other set has acquired from. As a comparison, referringto FIG. 1C, the two different sets of coupled collimator and detectorare not exactly opposite but offset by half of the sweeping step. Forexample, if the sweeping step is 6°, the directions 154A and 154B inwhich the two sets point towards may form an angle Y that is about 3°.Having an offset between the directions the two sets are pointingtowards allows the system 100 to acquire each image from a differentangle. For example, at a sweeping step of 6° and an offset of 3°, thefirst set may acquire images at angles 0°, 6°, 12°, . . . , 180°, 186°,. . . , 354° in sequence; the second set may acquire images at angles183°, 189°, 195°, . . . , 357°, 3°, . . . , 177° in sequence.

Reference is now made to FIGS. 11A and 11B. In a radiation-based imagingsystem, the performance is optimized when apertures of a collimator arealigned with sensing pixels of a detector. FIG. 11A illustrates a topview in the X-Y plane of a portion of an exemplary SFI collimator 203 (abasic pattern as shown in FIG. 6B) superimposed on a detector 204. FIG.11B illustrates a schematic cross-sectional view in the X-Z plane of aportion of the collimator 203 and the detector 204 along the A-A cut inFIG. 11A. The detector 204 as illustrated in FIGS. 10A and 10B includesan array of discrete sensing pixels 214. The discrete sensing pixels 214may be based on CZT or SiPM structures. Typically, the sensing pixels214 are arranged in a grid network (also referred to as the pixel grid)formed in rows and columns, such as the rows i=1, 2, 3, . . . andcolumns j=1, 2, 3, . . . in the illustrated embodiment. Any sensingpixel 214 located at a position (x, y) in the X-Y plane can berepresented by an index (i, j) (i and j are integers) in the gridnetwork and has a corresponding aperture (or a closed aperture in acoded pattern or a septum) in the grid network of the collimator 203(also referred to as the aperture grid). Since the sensing pixels 214 inFIGS. 11A and 11B are discrete and physically distinctive from eachother, to achieve alignment between a detector and a collimator isstraightforward, that is to position the sensing pixels 214 directlyunder the corresponding apertures 208 of the collimator 203 such thatthe pixel grid and the aperture grid overlap.

Reference is now made to FIGS. 12A and 12B. As discussed above inassociation with FIGS. 3 and 4 , in some embodiments, sensing pixels ofa detector are not physically distinctive from each other and are mereresults of digitization of a continuous detector surface, as in the caseof most PMT-based detector systems. FIG. 12A illustrates a top view inthe X-Y plane of a portion of an exemplary SFI collimator 203 (a basicpattern as shown in FIG. 6B) superimposed on such a detector 204. FIG.12B illustrates a schematic cross-sectional view in the X-Z plane of aportion of the collimator 203 and the detector 204 along the A-A cut inFIG. 12A. The detector surface is digitized as a pixel grid that is thesame as the corresponding aperture grid of the collimator 203, i.e., ofthe same interspacing between grid points. In other words, each pixelgrid unit on the detector surface has a corresponding aperture (or aclosed aperture in a coded pattern or a septum) in the collimator 203,which is the nearest. Each pixel grid unit on the detector surface isalso referred to as a pixel of the detector. The pixels of the detectorare arranged in a grid network formed in rows and columns, such as therows i=1, 2, 3, . . . and columns j=1, 2, 3, . . . and can be label aspixels (i, j) (i and j are integers). Ideally, under a perfectalignment, the pixel grid of the detector and the aperture grid of thecollimator should overlap. However, as shown in FIGS. 12A and 12B, quiteoften a misalignment may occur between the pixel grid and the aperturegrid, such as during apparatus assembly, resulting in misalignment inX-direction (denoted as Δx) and/or in Y-direction (denoted as Δy). Themisalignment introduces degradation to the system. For example, asillustrated in FIG. 12B, an incident photon 230 traveling through anaperture of the collimator 203, which is supposed to be recorded as anevent (e.g., a count) occurred at pixel (3, 1) under perfect alignment,would be instead recorded as an event occurred at pixel (3,2), thereforedecreasing the contrast of aperture pattern in the recorded signal.

Taking a detector system based on photomultiplier tubes (PMT) as anexample, where detector systems based on other structures are similar,briefly, the PMT functions by converting incident photons intophoto-electrons at the photocathode. These electrons produce a largenumber of secondary electrons from a series of charged cathodes,generating a measurable current pulse at the anode. Based on thesemeasurable current pulses in neighboring PMTs, a position (x, y) in thecontinuous X-Y plane can be determined as where the photon incidentevent occurs. Based on a mapping between the continuous X-Y plane andthe (i, j) indices, an event occurred at the position (x, y) issubsequently digitized as an event occurred in pixel (i, j). However, asdiscussed above, due to misalignment relying on an initial mappingbetween the continuous X-Y plane and the (i, j) indices may introduceperformance degradation. Image contrast provides a way of tuning tooffset misalignments. In order for an image to be perceivable by thehuman eye and mind, the array of pixels of the acquired image mustdisplay contrast. Something about the specimen must produce changes inthe signal intensity recorded at different pixels. At its simplest,transmission contrast may be due to structures that are partially orfully opaque, such as the apertures and closed apertures (or septa) of acollimator. The amount of contrast present in the image determines theaccuracy with which it is critical to adjust the misalignment. A setupto offset the misalignment by algorithm without physically moving acollimator is illustrated in FIG. 13 . In FIG. 13 , a flood source 242,such as a Co-57 or Tc-99m rectangular flood source, provides a uniformfield of radiation above the collimator 203. The flood source 242 can bepositioned tightly coupled to the collimator 203, that is being lessthan half of a thickness of the collimator including the instance wherethe collimator 203 and the flood source 242 are in physical contact.Under the illumination of the flood source 242, the acquired image fromthe detector 204 is an image of the flood source 242 shadowed by thecollimator 203. Due to the uniform radiation, the contrast in theacquired image is due to the transparent and opaque features of thecollimator 203. In other words, the pixels underneath closed apertures(or septa) or small apertures yields weaker image signal intensitycompared to the pixels underneath open or large apertures.

Contrast can be defined as a measure of the variation (e.g., a ratio oran absolute difference) of image single intensity between peak andvalley. As an example, a signal intensity line 244 in FIG. 13illustrates signal intensities V_(p) and V_(v) corresponding to a peakand a valley. One way to maximize contrast is to maximize the ratio ofV_(p)/V_(v), or to maximize the difference of |V_(p)−V_(v)|/V_(p). Whenthe contrast is maximized, the alignment between the collimator and thedetector is considered as being achieved.

Since the detector surface is digitized into a pixel grid, offsettingthe misalignment—in other words, maximizing contrast—can be achieved byan algorithm without a need to physically move the collimator. In anexemplary method, each signal emerging from the detector surface (e.g.,current pulses from PMT if in a PMT-based detector system) is recordedas an event with coordination (x, y). Thus, each entry in the data list(also referred to as list mode) is an attribute vector containinginformation about a single detected photon. For example, a stream ofevents may be labeled as (x_(n), y_(n)) (n=1, 2, 3, . . . ), where eachpair represents the X- and Y-coordinates of the n^(th) event detected.Based on a mapping between the continuous X-Y plane and the discrete (i,j) indices, the total counts reported in a pixel (i, j), denoted as C(i,j)), can be expressed asC(i,j)=Σ_(n=1) ^(N)δ(D(x _(n) ,y _(n))−(i,j))  (9)where D is the digitization function that maps an event occurred at (x,y) to a corresponding pixel (i, j), and δ function gives 1 if D(x_(n),y_(n)) is equal to (i, j), and 0 otherwise. Further, an energy windowmay be optionally applied to filter the events such that only when anevent occurred within the energy window will be counted. By definition,C(i, j) is the image signal intensity at pixel (i, j), representing thenumber of events that are recorded in the area covered by pixel (i, j),which is defined by the digitization function D. The signal intensitiesat peak and valley, V_(p) and V_(v), can be identified from the set ofC(i, j) (i=1, 2, 3, . . . ; j=1, 2, 3, . . . ) and an initial contrast(V_(p)/V_(v) or |V_(p)−V_(v)|/V_(p)) can be calculated.

Next, an offset pair (δx, δy) is introduced in the digitization functionto “offset” the pixel grid and recalculate C(i, j). Accordingly, C(i, j)can be expressed asC(i,j)=Σ_(n=1) ^(N)δ(D(x _(n) +δx,y _(n) +δy)−(i,j))  (10)where the introduction of (δx, δy) is equivalent to move the pixel gridin a distance of δx in the X-direction and a distance of δy in theY-direction. As a result, an event occurred at a position (x, y) thatwould otherwise be recorded under pixel (i, j) may be regarded asequivalently have occurred at a position (x+δx, y+δy) andcorrespondingly recorded under a neighboring pixel (i′, j′). The C(i, j)curve will thus be different and an updated contrast (V_(p)/V_(v) or|V_(p)−V_(v)|/V_(p)) is calculated. The optimal (δx, δy) can be found tomaximize the peak/valley contrast by a optimization method such assteepest decent, conjugate gradient, etc. An alternative is to create aseries of offset pairs (δx, δy) at a small step. By sweeping the seriesof offset pairs (δx, δy), one offset pair (δx, δy) with the maximumcontrast can be selected as the right offset amount to counter themisalignment, such as by regenerating the pixel grid. This offset pair(δx, δy) is termed selected offset pair or selected offset.Alternatively, the selected offset pair (δx, δy) can be applied tooffset the origin (x₀, y₀) of the X-Y plane to shift the whole pixelgrid (a special instance of regenerating the pixel grid). Ideally, theselected pair of (δx, δy) substantially equals the misalignment (Δx, Δy)but also depends on the sweeping steps used in generating the series ofoffset pairs (δx, δy). In various embodiments, the series of offsetpairs (δx, δy) can be generated from equally dividing pixel pitchesP_(x) (pitch in the X-direction) and P_(y) (pitch in the Y-direction),respectively. For example, for pixel pitches of 2.0 mm in both X- andY-directions, the set of offset pairs (δx, δy) can be a sweeping with astep of 0.2 um starting from 0 with δx<P_(x) and δy<P_(y), that is a setof {(0, 0), (0.2 mm, 0), (0.4 mm, 0) . . . (2.0 mm, 1.8 mm), (2.0 mm,2.0 mm)}. Other ways to generate the set of offset pairs (δx, δy) arepossible, such as by bubble sort algorithm, bucket sort algorithm,insertion sort algorithm, or other suitable algorithms.

Instead of sweeping δx and δy together, alternatively, the method maysweep in the X-direction alone (by fixing a δy) to get an optimizedoffset δx in the X-direction first, then sweep in the Y-direction alone(by using the optimized δx) to get an optimized offset δy in theY-direction subsequently. Or, similarly, the method may sweep in theY-direction first then in the X-direction. Further, instead of pickingV_(p) and V_(v) two dimensionally from the whole pixel grid to calculatecontrast, the method may pick a row (by fixing i in the set of C(i, j),such as the signal intensity line 244 in FIG. 13 ) and sweep (δx, δy) toget a maximized contrast in the row and apply the selected offset pair(δx, δy) to whole pixel grid. Or, similarly, the method may pick acolumn (by fixing j in the set of C(i, j) and sweep (δx, δy) to get themaximized contrast in the column and apply the offset pair (δx, δy) tothe whole pixel grid.

It is worth noting that different hole patterns may require differentoptimization approaches. In some patterns the maximum or minimum valuesof a descriptor (e.g., contrast, signal intensity at peak, or signalintensity at valley) of the recorded signal intensities may be used formaximization/minimization, such as a maximized contrast, a maximizedpeak value, or a minimized valley value. When repetitive hole patternsare used, corresponding pixels (corresponding to the same hole in thebasic pattern) may be added together to reduce the randomness (i.e.,quantum noise) in the pixel values. Also, in some embodiments whencertain hole pattern is used, the selected offset pair (δx, δy) from theoptimization routine, may be at a fixed offset away from the actualoptimum offset, and that fixed offset is determined by the hole pattern.For example, in some hole patterns, the maximum pixel value in a floodsource image is located in the middle of neighboring 2×2 open holes. Inthat case, the fixed offset is half a hole pitch, and the actual optimumoffset used to align pixels to holes would be corrected by the fixedoffset. In other words, after a selected offset pair (δx, δy) is found,a further step may be optionally performed to add or subtract a fixedoffset to or from the selected offset pair (δx, δy) in getting an actualoptimum offset to use for misalignment adjustment.

Although not intended to be limiting, one or more embodiments of thepresent disclosure provide many benefits for radiation-based imaging ofa target object, such as a patient. For example, a collimator designwith repetitive coded pattern that is spaced away from an associateddetector provides superior imaging resolution without sacrificing signalsensitivity. Therefore, system performance is improved.

The foregoing outlines features of several embodiments so that those ofordinary skill in the art may better understand the aspects of thepresent disclosure. Those of ordinary skill in the art should appreciatethat they may readily use the present disclosure as a basis fordesigning or modifying other processes and structures for carrying outthe same purposes and/or achieving the same advantages of theembodiments introduced herein. Those of ordinary skill in the art shouldalso realize that such equivalent constructions do not depart from thespirit and scope of the present disclosure, and that they may makevarious changes, substitutions, and alterations herein without departingfrom the spirit and scope of the present disclosure. Accordingly, it isappropriate that the appended claims be construed broadly and in amanner consistent with the present disclosure.

What is claimed is:
 1. A radiation-based imaging system, comprising: acollimator configured to filter radiation emitted from a target object,the collimator including a plurality of apertures non-uniformlydistributed on the collimator, wherein a largest acceptance angle of theplurality of apertures is not larger than 15°, and the plurality ofapertures forms an aperture pattern that includes a basic pattern thatis repeated more than four times within the aperture pattern; and adetector for detecting the radiation that has passed through thecollimator, wherein the collimator is spaced from the detector such thata point on a top surface of the detector that faces the collimator issimultaneously illuminated by two or more of the plurality of apertures,and wherein the collimator remains still relative to the detector duringdetection.
 2. The radiation-based imaging system of claim 1, wherein thepoint on the top surface of the detector is simultaneously illuminatedby a percentage of the plurality of apertures, wherein the percentage isless than 25%.
 3. The radiation-based imaging system of claim 1, whereinan amount of the plurality of apertures exceeds one thousand.
 4. Theradiation-based imaging system of claim 1, wherein the plurality ofapertures varies at least in one of aperture size, aperture shape,acceptance angle, length, and aperture pitch.
 5. The radiation-basedimaging system of claim 1, wherein a distance between the collimator andthe detector is from 1.5 to 10 times of a thickness of the collimator.6. The radiation-based imaging system of claim 1, wherein the basicpattern is a coded aperture pattern.
 7. The radiation-based imagingsystem of claim 1, wherein an illuminating area of one of the aperturesis within a range of +/−10% of an area of the basic pattern.
 8. Theradiation-based imaging system of claim 1, wherein the collimatorincludes a first portion and a second portion, wherein the first portionincludes through-holes uniformly distributed on the first portion andthe second portion includes through-holes non-uniformly distributed onthe second portion and corresponding to the plurality of apertures, suchthat a portion of the through-holes of the first portion is blocked bythe second portion.
 9. The radiation-based imaging system of claim 8,wherein a thickness of the first portion is from 2 to 10 times of athickness of the second portion.
 10. The radiation-based imaging systemof claim 1, wherein the collimator is a first collimator and thedetector is a first detector, further comprising: a second collimator;and a second detector coupled to the second collimator, wherein thesecond collimator is attached to the second detector.
 11. Aradiation-based imaging system, comprising: a first collimatorconfigured to filter radiation emitted from a target object, the firstcollimator including a first plurality of apertures that forms a firstaperture pattern; a first detector associated with the first collimatorfor detecting the radiation that has passed through the firstcollimator; a second collimator configured to filter the radiationemitted from the target object, the second collimator including a secondplurality of apertures that forms a second aperture pattern, wherein thesecond plurality of apertures are non-uniformly distributed on thesecond collimator, a largest acceptance angle of the second plurality ofapertures is not larger than 15°, and the second aperture patternincludes a basic pattern being not less than 3×3 in size andperiodically repeated more than four times within the second aperturepattern; and a second detector associated with the second collimator fordetecting the radiation that has passed through the second collimator,wherein the target object is positioned between the first collimator andthe second collimator, wherein the first aperture pattern is differentfrom the second aperture pattern, and wherein the second collimatorremains still relative to the second detector during detection.
 12. Theradiation-based imaging system of claim 11, wherein the first collimatoris in contact with the first detector.
 13. The radiation-based imagingsystem of claim 12, wherein a distance between the second collimator andthe second detector is from 1.5 to 7 times of a thickness of the secondcollimator.
 14. The radiation-based imaging system of claim 11, whereinthe first plurality of apertures is uniformly distributed on the firstcollimator.
 15. The radiation-based imaging system of claim 11, whereinthe basic pattern includes a coded pattern.
 16. The radiation-basedimaging system of claim 15, wherein the coded pattern is one of auniformly redundant array (URA) pattern, a modified uniformly redundantarray (MURA) pattern, and a perfect binary array (PBA) pattern.
 17. Theradiation-based imaging system of claim 15, wherein a normal directionto a top surface of the first detector and a normal direction to a topsurface of the second detector form a non-zero angle.
 18. An apparatusfor medical imaging, comprising: a plate with a top surface and a bottomsurface and holes extending from the top surface to the bottom surface,wherein the holes are arranged as repetition of a basic pattern, andwherein the basic pattern is a coded pattern; and a detector configuredto acquire an image from photons passing through the holes in the plate,wherein the plate has a thickness, wherein a spacing between the plateand the detector is at least 1.5 times of the thickness of the plate,and wherein the collimator remains still relative to the detector duringdetection.
 19. The apparatus of claim 18, wherein the basic pattern hasa grid of an odd number of rows and an odd number of columns.
 20. Theapparatus of claim 18, wherein an illuminating area of one of the holesis within a range of +/−10% of an area of the basic pattern.